Superconductor-insulator duality for the array of Josephson wires

TL;DR

This paper introduces a new model of Josephson wire arrays to study superconductor-insulator transitions, deriving an exact duality transformation and analyzing phase diagrams with respect to various parameters and frustrations.

Contribution

It develops a novel theoretical model for Josephson wire arrays, including an exact duality transformation and phase diagram analysis under different conditions.

Findings

Derived an exact duality transformation for the model.

Calculated critical parameters for phase transitions at different frustrations.

Estimated transition temperatures and phase boundaries in the presence of disorder.

Abstract

We propose novel model system for the studies of superconductor-insulator transitions, which is a regular lattice, whose each link consists of Josephson-junction chain of $N \gg 1$ junctions in sequence. The theory of such an array is developed for the case of semiclassical junctions with the Josephson energy $E_J$ large compared to the junctions's Coulomb energy $E_C$. Exact duality transformation is derived, which transforms the Hamiltonian of the proposed model into a standard Hamiltonian of JJ array. The nature of the ground state is controlled (in the absence of random offset charges) by the parameter $q \approx N^2 \exp(-\sqrt{8E_J/E_C})$, with superconductive state corresponding to small $q < q_c $. The values of $q_c$ are calculated for magnetic frustrations $f= 0$ and $f= \frac12$. Temperature of superconductive transition $T_c(q)$ and $q < q_c$ is estimated for the same values of $f$. In presence of strong random offset charges, the T=0 phase diagram is controlled by the parameter $\bar{q} = q/\sqrt{N}$; we estimated critical value $\bar{q}_c$.